0:14 Can you hear me? Yeah, my name is Johannes Müller-Römer. I am representing the Fraunhofer Institute for Computer Graphics Research IGD today with our project SubSimX. And in SubSimX, our goal was to basically bring subdivision modeling and finite element analysis close together so that it really becomes a real-time structural design medium. So, we all want to do generative and simulated simulation-driven engineering. And well, first thing we typically do is we will structurally evaluate some initial designs.

0:56 And then, after we have selected our specific design, we will still iteratively optimize that. And there might be different optimization goals. The main one we’re looking at here is a weight versus stiffness. And basically, we’re looking for an optimal design for some given boundary conditions. Now, this design analysis tends to be fairly slow in practice due to several bottlenecks. So, for one, when we start with a B-rep from your traditional CAD program, NURBS trimmed NURBS, first, generating mesh from that for simulation, high-quality mesh, is fairly expensive.

1:39 Then, typically, since you’re switching between tools, things like face IDs might not be preserved, especially if you’re switching between tools from different vendors. And you might have to set up your boundary conditions every single time you’re doing it. Simulation itself tends to be somewhat slow as well. So, the question is, how can we integrate the structural simulation and modeling tightly enough to actually have it simulation accompanying and steering the model modeling process?

2:18 So, the current workflow from a simplified view is you take your initial guess, no matter where it comes from, if it’s from topology optimization or if it’s coming from some generative or AI tool, then you’ll typically remodel that into some manufacturable design in your CAD program. You can use subdivision modeling for that or nerves. And in the end you want something that’s manufacturable by 3D printing or casting, for example.

2:54 And then you iterate. So, you generate your FEA mesh, you set up your boundary conditions, you simulate, and then you also post-process and visualize that to actually find out what’s happening. And well, finally you modify your model and repeat everything until you’re satisfied with the result. And from talking with yeah, industry partners, yeah, we found out that many of them are using separate tool for pretty much everything and they have a bunch of media breaks in between there.

So, they often need manual import and export between these tools, setting up things again and again and again, every time wasting minutes, hours on every iteration. Now, this leads well, to slow iterations. And so, you either do just a handful of iterations and get a result that’s just not optimal, or you do a whole bunch of iterations, spending ages on that, but you get a really good result.

3:53 Now, this slow iteration actually prevents the routine use of topology optimization and AI-driven exploitation in daily engineering practice. So, what we really want is some form of being construction with interactive FEA, a structurally aware modeling environment, and we want want the designers to be able to work with the tools they’re familiar with. So, with the representations they’re used to, for example, subdivision surfaces, and with dedicated modeling software.

4:28 And of course, we want this direct simulation feedback. So, basically, we’re looking for a shortcut here. Now, what we want to do with our interactive FEA is basically we only want to do the FE mesh generation once, at the very beginning. Then, we only want to set up our boundary conditions once, and then what we do is we precompute a volumetric mapping so that the vertices in the finite element mesh are directly coupled to the vertices in the control mesh.

5:03 So, the iteration is basically the same as before. You’ve got your simulation, you’ve got your post-processing visualization. You can modify your model, update the finite element mesh and boundary conditions, but the big difference most of these steps are now fully automated. You don’t have to switch tools anymore. They’re just both open at the same time, and you see your results almost immediately. So, the biggest component here in SubsimX was the volumetric mesh morphing, and we use Catmull-Clark subdivision surfaces, and the surface is defined by a control mesh, and each surface vertex is, in fact, a weighted sum of the control points.

5:52 Now, this gives us a direct surface mapping. So, for every point on the surface, on the limit surface of the subdivision mesh, we can directly tell you, “Okay, that that’s this weighted sum.” And, if the control mesh is deformed, the surface mesh follows. Now, how do we extend this to the finite element mesh? Well, first, we generate an FE mesh from this initial surface. Then, the surface weights are propagated into the volume.

6:25 And, by doing that, we obtain a precomputed volumetric mapping, where each FE node is basically just the weighted sum of the control points. So, whatever you as long as you only change positions of your mesh, and you’re not changing your topology of your control mesh, you don’t need to, recompute anything. You can just reuse the mesh. Of course, yeah, large edits may create low-quality tetrahedra. You might get inversions and things like that.

6:59 So, we also integrated a fast, robust local mesh repair step, which improves element quality while preserving mesh topology. And I’m talking about the high-level topology between the different faces that the designer is aware of. So, it’s not like the low-level, single triangles. It’s the actual surfaces, that the designer actually cares about. And this local, re- mesh repair step, looks as follows. Basically, it detects low-quality tetrahedra after large deformations.

7:29 So, we’re talking about small angles, inverted elements. And then, it applies a bunch of local operations, such as edge collapses, vertex smoothing, face flips, in parallel, because, well, we’re doing everything on the GPU because we want to be fast. And, yeah, this improves the element quality and it still preserves the connectivity and boundary condition assignment so that we don’t need to redo anything because the whole tool chain is aware of this concept of having multiple high-level faces.

8:06 And the result is we have the same analysis mesh and it can be adapted to many, many shape changes while remaining a valid mesh for finite element analysis. Now, fast mesh morphing and fixing that mesh is, of course, not the only component to very fast iteration because the other component is, of course, a very fast finite element solver. And what we use there is our own solver that’s called Ristra.

8:35 It’s a GPU-accelerated finite element solver. Yeah, it basically does everything on the GPU. Even the matrix assembly is not done on the GPU. And we and it’s fast and accurate. And what I mean by accurate is it’s basically produces numerically identical results to existing commercial solvers while being up to 100 times faster. And we even benchmarked against some GPU-accelerated commercial solvers and reached speedups of up to 30 because we just put much more on the GPU than your average FEA tool does.

Now, results, visualization, and multiple load cases are all features that are already built in. And you don’t really need any high-end hardware. So, that animation you see here, which is actually running slower than the actual simulation would be running, has 150,000 linear elements and it’s, yeah, 400 milliseconds per load case on a regular consumer GPU and in fact I think it was actually a mobile GPU as well.

9:45 So, we have this pipeline for for this interactive workflow and Sub Sim X, which is this one tool, basically connects the modeling software of choice where we have small plugin that basically triggers these updates and just sends the updated tools. We have Ristra, which does simulation and visualization and is embedded into Sub Sim X. And so, the steps per update are as follows. You’ve got the mesh morphing and remeshing.

10:14 You’ve got boundary condition transfer. You’ve got set up for Ristra. And yeah, well, we’ll solve everything and present the results. So, Sub Sim X drastically shortens this simulation loop compared to conventional workflows because well, many steps are only done once like finite element mesh generation and boundary condition setup. And others like the FEA solver and visualization are just much faster. So, for a typical iteration, we’re talking about going from minutes to hours to seconds to a few minutes.

10:52 And that includes the modeling that the designer does in the meantime. Yeah, so this gives us a really fast way of doing it and well, I’ll just show you a quick video. So, here we actually see Blender on the left, which was the the modeling tool of choice for our commercial partner, Bionic Mesh Design. And yeah, on the right we see Sub Sim X, which is currently has Ristra embedded into it.

11:31 So, here we’re seeing the solution. We can see this is a just a regular tetrahedral mesh as you’d use in any other FEA tool. But the nice thing is when you edit there, you almost immediately get a result on the right-hand side. Now, here we sped it up a little because otherwise this video would take a full 5 minutes. And yeah, so here my colleague is going through a bunch of iterations until he arrives at a model that he’s satisfied with with no problematic stress peaks while still maintaining a good weight-to-stiffness ratio.

12:17 And what you see here was actually done on an RTX 46 4060 mobile, so that’s why I presume that the 400 milliseconds my colleague gave me were from the same machine. Yeah, so right now the workflow we’re we’re supporting is that we basically take a topology mesh and move to a smooth manufacturable design. And well, we basically in this process you start with a topology optimized mesh.

12:52 You reconstruct it using a smooth subdivision control mesh. So, this remodeling step is something very common that well, almost always is required because in the end you want to have it in your CAD tool of choice. Then you use SubSimX for continuous shape optimization and manufacturability refinement and you In this case, you’re doing it manually, although there’s nothing stopping you from scripting that in some way as well.

13:25 So, one potential future workflow would be to integrate that with a generated generative design and scripted exploration. So, the idea would be to take many control mesh variants, either by using parametric meshes a script that uses a DSL to generate geometry, or just have some generative model, and then use SubSuf X to perform, yeah, quick evaluation of each variant. But also enabling dense design sweeps within each concrete design topology, right?

Because, the speed-ups from the, mapping, of course, apply to subdivision control meshes that maintain the same topology. Another variant might be to do AI in the loop structural feedback, where your AI proposes new subdivision control meshes, SubSuf X and Riskier compute structural scores, stiffness, stress, mass, and so on, and that you feed back these scores into the to guide the next generation of designs. Where you could where ideally, of course, you want to keep the same topology as well, for to achieve the full speed-up.

14:48 So, yeah, the main workflow up there, the one we’re currently using, as well as two potential future directions. So, in summary, we have seen that we now have a way to do rapid structural evaluation of many candidate shapes, so we can quickly explore the design space, we can do fast shape optimization, and we get structural feedback in seconds or even fractions of seconds, which, well, enables this, manual process where you edit and immediate will look at the result or the scripted design sweeps.

15:32 The whole thing is an integrated pipeline, so you don’t really have to switch between your tools. You’ve got your two tools, your editor open and well, your Sub-Sim X and most of the repetitive tasks are fully automated now and so the designer can work uninterrupted without media breaks, without exporting, importing, resetting boundary conditions. And well, which brings us to our goal of better designs in a shorter time.

16:08 And yeah, from structural updates on the order of seconds instead of minutes to hours for conventional workflows. Yeah, so basically going from the model on the left to the model on the right, which was took 5 minutes. And otherwise, the only thing I have left is my contact information in case anyone has questions. To learn more about the CFD fan computational design symposium, access the archive of previous presentations, interviews with speakers, and information about future events around the world, visit CDFAM.com.